What is the solution for y^{''}-13y^'-42y=0 ?

The solution for y^{''}-13y^'-42y=0 is y=c_{1}e^{((13+sqrt(337))t)/2}+c_{2}e^{((13-sqrt(337))t)/2}

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y^{''}-13y^'-42y=0

y^{^{''}} - 13 y^{^{'}} - 42 y = 0

y = c_{1} e^{\frac{( 13 + 337 ) t}{2}} + c_{2} e^{\frac{( 13 - 337 ) t}{2}}

Solution steps

y^{''} (t) - 13 y^{'} (t) - 42 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 13 + 337 ) t}{2}} + c_{2} e^{\frac{( 13 - 337 ) t}{2}}

y = c_{1} e^{\frac{( 13 + 337 ) t}{2}} + c_{2} e^{\frac{( 13 - 337 ) t}{2}}

43 y^{^{'''}} - 13 y^{^{''}} + 42 y^{^{'}} = 0

x^{^{''}} + 12 x^{^{'}} + 40 x = 0, x (0) = 0, x^{^{'}} (0) = 4

13 y + 6 y^{^{'}} + y^{^{''}} = 0

y^{^{'''}} + (- 3) y^{^{''}} + 3 y^{^{'}} - y = 0

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y (0) = 3, y^{^{'}} (0) = - 3

What is the solution for y^{''}-13y^'-42y=0 ?
The solution for y^{''}-13y^'-42y=0 is y=c_{1}e^{((13+sqrt(337))t)/2}+c_{2}e^{((13-sqrt(337))t)/2}